Are ICMP packets not important for a hosted machine?

[Ron Varburg]

A Hosting service is blocking pings from the Internet to the hosted servers.
It is possible to ping from the hosted servers to anywhere on the Internet,
assuming that the packets are not dropped somewhere else, ofcourse.
1. Why would the hosting service bother with such a blockage?
2. Is it reasonable to assume that more ICMP packets are blocked?
3. What are the implications of such a blockage? In particular,
   assuming that each hop in a random path takes care to assure
   connectivity to any nearest hop, one might think that ICMP packets
   are not important and hardly used.